Question

Use the laws of Sines and law of cosines to find missing dimensions​

Answer 1

Answer:

A) ERROR

B) ∠C = 26°

Step-by-step explanation:

Houston, We have a problem!!! too much information

If we had a legit triangle, the law of sines would hold

19/sin138 = 8/sin20

  28.395 = 23.390

as this is NOT an equality, the triangle does not exist as described.

IF it did, we'd get different results depending on which set we used

∠F = 180 - 138 - 20 = 22°

Law of sines

19/sin138 = DE/sin22 ⇒ DE = 19sin22/sin138 = 10.63697...

or

8/sin20 =  DE/sin22 ⇒ DE = 8sin22/sin20 = 8.762211...

If we attempt to use Law of cosines

DE² = 19² + 8² - 2(19)(8)cos22 = 11.9639...

so really none is correct because we attempt to use trig calculations to a non-triangle.

12) AC² = 15² + 19² - 2(15)(19)cos120

      AC = 29.51270...

29.51270 / sin120 = 15/sinC

C = arcsin(15sin120/29.51270) = 26.1142... 26°

Answer 2

9514 1404 393

Answer:

  11. inconsistent information

  12. 26°

Step-by-step explanation:

11. The given numbers are inconsistent. (The first attachment shows one of the 4 possible solutions.)

__

12. In order to find angle C, we need to know side AC. We can find that using the Law of Cosines.

  b = √(a² +c² -2ac·cos(B)) = √(19² +15² -2(19)(15)cos(120°)) = √871

  b ≈ 29.513

Then angle C is found from the Law of Sines.

  C = arcsin(c/b·sin(B)) = arcsin(15/29.513·sin(120°)) ≈ 26.11°

Angle C is about 26°.

The second attachment shows the output of a triangle solver.